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topology > general topology > adjunction space
geometry > topological space > adjunction space

Preferred term

adjunction space  

Definition

  • In mathematics, an adjunction space (or attaching space) is a common construction in topology where one topological space is attached or "glued" onto another. Specifically, let X and Y be topological spaces, and let A be a subspace of Y. Let f : AX be a continuous map (called the attaching map). One forms the adjunction space Xf Y (sometimes also written as X +f Y) by taking the disjoint union of X and Y and identifying a with f(a) for all a in A. Formally,


    where the equivalence relation ~ is generated by a ~ f(a) for all a in A, and the quotient is given the quotient topology. As a set, Xf Y consists of the disjoint union of X and (YA). The topology, however, is specified by the quotient construction.
    Intuitively, one may think of Y as being glued onto X via the map f.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Adjunction_space)

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http://data.loterre.fr/ark:/67375/PSR-D0STC250-J

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